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Estimation of glacial melt contributions to the Bow River, Alberta,
Canada, using a radiation–temperature melt model
Eleanor A. BASH,Shawn J. MARSHALL
University of Calgary, Calgary, Alberta, Canada
E-mail: ebash@mtroyal.ca
ABSTRACT. Alberta’s Bow River has its headwaters in the glaciated eastern slopes of the Canadian
Rockies and is a major source of water in southern Alberta. Glacial retreat, declining snowpacks and
increased water demand are all expected in the coming century, yet there are relatively few studies
focusing on quantifying glacial meltwater in the Bow River. We develop a new radiation–temperature
melt model for modelling distributed glacier mass balance and runoff in the Bow River basin. The model
reflects physical processes through the incorporation of near-surface air temperature and absorbed
radiation, while avoiding problems of collinearity through the use of a radiation-decorrelated
temperature index. The model is calibrated at Haig Glacier in the southern portion of the basin and
validated at Haig and Peyto Glaciers. Application of the model to the entire Bow River basin for 2000–09
shows glacier ice melt is equivalent to 3% of annual discharge in Calgary on average. Modelled ice melt
in August is equal to 8–20% of the August Bow River discharge in Calgary. This emphasizes the
importance of glacier runoff to late-summer streamflow in the region, particularly in warm, dry years.
KEYWORDS: glacier discharge, glacier modelling, melt – surface, mountain glaciers
INTRODUCTION
Snowmelt and glacier melt are essential sources of fresh
water in western Canada and are strongly affected by
climatic conditions (Barnett and others, 2005). Glaciers have
the unique ability to store water in years of high snowfall
and low temperatures, while supplementing streamflow in
years of lower snowfall and higher temperatures (Fountain
and Tangborn, 1985). Declines in Rocky Mountain snow-
pack are expected to continue with changing climate
(MacDonald and others, 2012), and mean annual tempera-
tures are expected to increase (Schindler and Donahue,
2006). These factors will further contribute to the glacial
retreat that has been observed in the Canadian Rockies since
the mid-20th century (e.g. Demuth and others, 2008; Bolch
and others, 2010; Tennant and others, 2012). The South
Saskatchewan River and its tributaries in southern Alberta,
including the Bow River, are believed to be particularly
vulnerable to declining mountain runoff (e.g. Rood and
others, 2005, 2008); the river system is fully allocated,
mainly for irrigation purposes. The combined effect of these
influences will be future increases in water stress in southern
Alberta, particularly in light of increasing demand.
Several studies have attempted to quantify glacial
contributions to streamflow in the Bow River basin, on the
eastern slopes of the Rocky Mountains. Hopkinson and
Young (1998) examined statistical relationships between
changes in glacier volume and streamflow for the upper Bow
River basin. They reported annual glacier contributions to
the Bow River at Banff, Alberta, of 2% on average,
between 1952 and 1993. In extremely dry years, they found
that glacier volume loss provided up to 50% of late-summer
flow in the Bow River at Banff. They also found that
significant long-term glacier volume loss reduced the
buffering capacity of glaciers in times of low flow.
Demuth and others (2008) focused on mass-balance and
volume reconstructions of benchmark glaciers in the south-
ern and northern Cordillera, specifically Peyto Glacier
located just north of the Bow River basin. They found that
small glaciers showed a marked decrease in volume over the
20th century, as well as negative mass-balance trends since
1880. According to the study, this has led to decreased flows
in the Nelson River system, of which the Bow is a sub-basin.
The hydrological model WATFLOOD was used by Comeau
and others (2009) to estimate glacial and snowmelt
contributions to the Bow River from 1975 to 1998. They
concluded that shifts in flow timing will be the main impact
of future glacier recession on streamflow and expect this to
manifest as earlier peak flows and lower flows in late
summer. Marshall and others (2011) used a combination of
simplistic models of glacier mass balance and glacier
dynamics to estimate glacial contributions to streamflow
along the eastern Rocky Mountain front. Marshall and others
(2011) provided the only estimate of future glacial contribu-
tions to the Bow River.
The language used to describe glacier melt varies greatly
between studies. For the purpose of this study, we refer to
snowmelt, ice melt and volume loss. During the course of
any melt season, exposed glacier ice melts; in this study,
snowmelt refers to melting of seasonal snow (i.e. the winter
snowpack) and ice melt includes any melting of exposed ice
or firn (i.e. multi-year snow and ice that has been stored on
the glacier). Volume loss refers to the ice melt which is a
result of negative mass balance. In years of negative mass
balance, ice melt will generally be higher than volume loss,
because some snow in the accumulation area of the glacier
goes into storage. In years of positive mass balance, there is
no volume loss, but ice melt will still occur. Snowmelt in our
study includes melt of all snow from glacier surfaces, but not
the surrounding terrain.
The future of water management in southern Alberta will
depend on reliable knowledge of glacial meltwater re-
sources in the region. While the current body of knowledge
Annals of Glaciology 55(66) 2014 doi: 10.3189/2014AoG66A226
*Present address: Mount Royal University, Calgary, Alberta, Canada.
138
provides some insight, there is a need for better under-
standing in order to inform water management. This study
develops a new distributed melt model to estimate glacial
contributions to the Bow River in the early 21st century.
STUDY AREA
Bow River basin
The Bow River basin, located in southern Alberta, is a sub-
basin of the South Saskatchewan River, part of the larger
Nelson drainage system. The headwaters are on the contin-
ental divide in the Eastern Front Range of the Canadian
Rocky Mountains and the river runs east roughly 400 km
before joining the North Saskatchewan River (Fig. 1). There
are several population centres in the basin, including the
city of Calgary and the towns of Banff, Canmore and
Cochrane. In addition to municipal water uses, there are
high agricultural water demands. Of the annual flow in the
South Saskatchewan, 60–70% is allocated through provin-
cial permits, and the basin is now closed to further
allocations (http://environment.alberta.ca/01722.html). A
number of glaciers supplement water flow in the Bow River,
most notably Bow and Crowfoot Glaciers, which are outlets
of the Wapta Icefield.
The largest contiguous ice mass in the basin is 11 km
2
,
and includes the two above-mentioned glaciers, as well as a
portion of the icefield. For the purpose of this study, only ice
bodies 0.1 km
2
were included. With this stipulation, 73 ice
bodies were identified in the basin, covering 57 km
2
. The
average area of these glaciers is 0.8 km
2
. The glaciers of the
basin span an elevation range of 1900–3500m, with 74% of
glacier area existing between 2500 and 2900 m.
Peyto Glacier, another outlet of the Wapta Icefield
feeding the North Saskatchewan River basin, has been
monitored by different agencies of the Government of
Canada since 1966. Though it does not feed into the Bow
River, it is within a few kilometers of the Bow River
headwaters, and the extensive data record at Peyto Glacier is
useful for comparison purposes in this study. Peyto Glacier is
12 km
2
and has an elevation range of 2100–3150 m
(Hopkinson and others, 2010). This spans the elevation
range of most glacier coverage in the basin.
Basin-wide analysis is based on a digital elevation model
(DEM) developed by Christina Tennant at the University of
Northern British Columbia (UNBC). The DEM is based on
Shuttle Radar Topography Mission 3, which was resampled
to 100 m resolution. Glacier inventory data, based on
Landsat imagery from 2004–06, are used to delineate glacier
coverage in the basin. The inventory was generated and
manually checked in 2008 (Bolch and others, 2010). It
includes ice bodies of at least 0.05 km
2
.
Daily meteorological data for Banff, as well as monthly
temperature data from Banff and other stations, were
downloaded from Environment Canada (http://www.clima-
te.weatheroffice.gc.ca/climateData/canada_e.html). Ar-
chived snow pillow and snow depth data are collected by
Alberta Environment. Mass-balance data from Peyto Glacier
were obtained through the World Glacier Monitoring
Service. Winter, summer and annual balance are reported
at Peyto Glacier until 1995, after which only net-annual
balance is reported.
Regional cloud cover is available at a resolution of
210 km as part of the US National Centers for Environmental
Prediction (NCEP) Reanalysis data, provided by the US
National Oceanic and Atmospheric Administration Physical
Sciences Division (Kalnay and others, 1996).
Hydrometric data were obtained for the Bow River at
Banff and Calgary. Historical daily discharge at Banff from
1912 to 2009 was downloaded from the Water Survey of
Canada (http://www.wsc.ec.gc.ca/hydat/H2O/index_e.cfm).
Mean weekly discharges and naturalized discharges at
Calgary were obtained from Alberta Environment (Water
Sciences Branch, unpublished).
Haig Glacier
Haig Glacier lies in the southern portion of the Bow River
basin on the eastern slopes of the Canadian Rocky
Mountains, 100 km southwest of Calgary. Sloping gently
southeast from the British Columbia–Alberta border, it spans
an elevation range of 485m, from 2435 to 2920m at the
continental divide, and has a total area of 2.8 km
2
. Haig
Glacier is the largest outlet of a small icefield, which also
includes French Glacier to the north and an unnamed
glacier to the west. Though it is slightly larger than the
average glacier in the basin, Haig Glacier, like Peyto Glacier,
spans the elevation range of most glacier coverage in the
basin. The median elevation of Haig Glacier is 2662m,
compared with 2620 m for the median elevation of all
glaciers in the Bow River basin (Marshall and others, 2011).
Combined with the availability of data, this glacier provides
a good setting for development of modelling techniques for
use over the entire basin.
Haig Glacier has been a site of ongoing glaciological
study since 2001, including mass-balance surveys, runoff
monitoring and measurement of meteorological variables.
An automatic weather station (AWS) is situated at 2600m,
roughly coinciding with the equilibrium line, while a second
is situated in the glacier forefield at 2335 m. Each AWS
consists of a Campbell Scientific CR1000 data logger, solar
panel, anemometer, four-component radiometer, tempera-
ture and humidity sensor in a radiation shield, and ultrasonic
distance sensor. In addition, the forefield AWS has both a
Fig. 1. The Bow River basin, southern Alberta, has headwaters on
the continental divide in the Eastern Front Range of the Canadian
Rocky Mountains. Haig Glacier, indicated in the southern portion
of the basin, has been the focus of ongoing glaciological study,
including mass-balance and meteorological measurements.
Bash and Marshall: Glacial melt contributions to the Bow River 139
pressure sensor and a rain gauge. The forefield station is set
up on an aluminum tripod, while the glacier station is
mounted on a mast drilled into the ice. The glacier station
has migrated over time with the movement of the glacier and
periodically must be redrilled due to melting out, which at
times leads to leaning of the mast. As a result of this, the
glacier station has a number of data gaps. Both stations
collect data at 10 s intervals and record 30 min averages.
Winter balance surveys were conducted each year (2002–
10) between late April and early June, consisting of centre-
line depth measurements and two to four snowpack density
profiles. Significant wind redistribution was observed during
the surveys. Melt measurements were collected along the
centre line periodically throughout most summers to give an
ongoing picture of melt over the course of a given season.
The snow accumulation and mass-balance regime for Haig
Glacier are discussed in Adhikari and Marshall (2013).
MELT MODEL
In this section we describe the theoretical basis of the melt
model, the data sources used to constrain and evaluate the
model, and the methods deployed to extend the model to the
Bow River basin. There are three stages to the model develop-
ment: (1) model calibration at the Haig Glacier AWS site;
(2) extension to a distributed snow accumulation and melt
model for Haig Glacier, based on far-field meteorological
data and cloud cover from a climate model; and (3) extension
of this simplified distributed model, which has no in situ
meteorological or glaciological data requirements, to the
Bow basin. The methods section explains each stage of model
development, and model calibration (optimized parameters)
and performance assessment are discussed in the results.
Theory
Given the basin-wide scope of this study, we focus on
developing a physically based melt model that does not rely
heavily on measured data. While a full energy-balance
model would be ideal for understanding melt processes, the
heavy data requirements make it a poor choice for large-
scale modelling, such as that undertaken in this study.
Degree-day models, in contrast, provide a model with few
data requirements, but lose some of the detail of energy-
balance models, particularly in complex terrain where solar
radiation inputs are highly variable.
Temperature-index models incorporating solar radiation
have been shown to perform equally with full energy-
balance methods in regional-scale studies (Hock, 2005). In
addition, temperature-index methods are simpler to apply to
catchment- or regional-scale melt modelling, where high-
resolution meteorological inputs needed for more complete
energy-balance models are difficult to obtain. The enhanced
temperature-index model (Hock, 1999), which includes
potential direct clear-sky radiation, is probably the most
widely used for distributed melt modelling (e.g. Verbunt and
others, 2003; Zappa and others, 2003; Huss and others,
2008). Pellicciotti and others (2005) discussed shortfalls of
this model, most importantly the incorporation of a
simplistic reflectance term, rather than true surface albedo.
Snow and ice albedo vary dramatically throughout the melt
season, and changes in albedo can account for a significant
proportion of melt by increasing or decreasing absorbed
radiation. In addition, the radiation factor is based on
potential direct rather than actual solar radiation, so the
model is not sensitive to varying cloud conditions at different
sites or through the melt season. The Hock (1999) model is
essentially a degree-day model, with the melt factor varying
in space based on potential radiation. Alternatively, treating
radiation and temperature separately allows the influence
of each to be treated independently (Pellicciotti and
others, 2005).
Both Anslow (2004) and Pellicciotti and others (2005)
present a modification of the temperature-index model by
including measured albedo and incoming (surface-level)
solar radiation in a melt model. This modification makes for
a more complex model, but begins to bridge the gap
between energy-balance and degree-day models. With
separated absorbed radiation and temperature, the model
comes closer to treating melt as a physical, rather than an
empirical, process. A linear combination of these two
variables, however, must necessarily include overlapping
influence from the effect of radiation on temperature. This
relationship can be ignored in Hock (1999), because the
albedo and radiation terms are included in the coefficient,
rather than as independent variables. Anslow suggested
removing the variance of temperature due to radiation by
regressing radiation on temperature. The residual of this
regression is the input to a new melt model. This method
was applied by Shea and others (2005), but not fully
explored. Building on the work of Anslow (2004), Pellicciotti
and others (2005) and Shea and others (2005), this study
explores a model using temperature and absorbed solar
radiation which addresses the problem of collinearity
pointed out by Anslow (2004).
Model formulation at Haig Glacier AWS
Four datasets from the summers of 2002–04 at the Haig
Glacier AWS are used to parameterize the relationship
between melt, temperature and solar radiation to model
summer melt at the location of the AWS. These are melt
(from an ultrasonic distance sensor), air temperature,
incoming and outgoing shortwave radiation. The melt model
development is restricted to the May–August period, the
main melt season at this site.
For model development and comparison, melt is deter-
mined by the change in snow depth or ice surface position
measured by an ultrasonic distance sensor at the AWS. To
calculate melt (M), the average depth at the beginning of a
melt period is subtracted from the average depth at the end
of the period. The change in depth (cm) is converted to
mm w.e. using the density of snow or ice. The densities of
both glacier ice and new snow are based on the median of a
range of values in Paterson (1994), with new snow set to
150 kg m
–3
and ice to 874 kg m
–3
. The density of old snow is
determined by relating the Julian day to densities measured
at Haig Glacier (i.e. snow age through the melt season,
which crudely accounts for snow densification and snow-
water content). Melt-season values range from 300 to
450 kg m
–3
.
Depth records are inherently noisy, and daily surface
height changes are of the order of a few cm, giving a low
signal-to-noise ratio, so depth changes were based on 5day
periods of melt, as opposed to daily or hourly changes. For
this reason, all other model variables described below were
aggregated to 5 day periods.
New snow events are identified as positive changes in
depth during the summer months using a time-series plot of
depth. These are isolated manually and snow accumulation
Bash and Marshall: Glacial melt contributions to the Bow River140
is calculated as the depth at the end of snowfall minus the
depth at the beginning of snowfall.
The amount of radiation absorbed at the glacier surface
(i.e. the energy available for melt) is calculated by subtracting
measured outgoing radiation from measured incoming radi-
ation. For aggregation into 5 day periods, daily absorbed
radiation (Iabs; MJ m
–2
d
–1
) is first calculated based on daily
total incoming and outgoing radiation. The total absorbed
radiation for each day is then summed into 5day periods.
Energy from absorbed shortwave radiation affects air
temperature in the glacier boundary layer, leading to close
linkages between these two measurements. Using daytime
temperature (08:00–20:00) and absorbed radiation data
from all three summer seasons, a relationship between the
variables is modelled through linear regression,
TI¼þIabs. The residual temperature, Tres, is determined
by subtracting TIfrom the near-surface air temperature, T,
for daytime hours. Tres is interpreted as the air temperature
due to heating other than solar radiation, such as longwave
radiation and sensible heat flux.
Half-hourly recorded temperature and daily absorbed
radiation values are used to calculate Tres, which is then
summed into 5 day positive degree-day totals (PDDres). By
using PDD in the model, temperatures below 08C have no
negative effect on melt (i.e. negative temperatures do not
decrease the amount of melt). The measured temperature is
also summed into 5 day PDD to assess whether temperatures
were >08C, enabling melt.
The variables described above are combined to form the
final melt model, where MF and RF are free parameters:
M¼MF PDDres þRF Iabs : PDD >0
0 : PDD 0
ð1Þ
In this form, times of melt and no melt are separated using
real air temperature. The residual temperature contributes to
melt at times when it is above zero, but all melt is attributed
to solar radiation when the residual temperature is negative
(PDDres ¼0).
The performance of the model is evaluated through a
comparison of measured and predicted melt for the 2007
summer season. Haig Glacier data from 2002 to 2004 are
also used to calibrate the model developed by Pellicciotti and
others (2005) and the results of both models are compared for
summer 2007 using the Nash–Sutcliffe coefficient:
N¼1PðMib
MiÞ2
ðMiMÞ2ð2Þ
where Mis 5 day measured melt, b
Mis modeled melt and M
is the average 5 day measured melt for the season. The
subscript irefers to the ith 5 day time-step in the model.
Distributed model formulation
The calibrated model described above is applied over the
surface of Haig Glacier using modelled inputs. The different
models used to estimate the inputs for Eqn (1) are described
below. Although we have detailed data from Haig Glacier,
we develop a basin-wide model for snow accumulation,
temperature, cloud cover and solar radiation, based on
meteorological observations at a distant ‘index site’ (Banff)
and US National Centers for Environmental Prediction
(NCEP) Reanalysis. Modelled fields can then be compared
with detailed measurements at Haig Glacier to assess the
performance of the regional model. This is of course inferior
to the actual data for modelling of Haig Glacier mass
balance, but it is a more suitable approach for regional-scale
and future modelling.
Several functions to predict initial snow depth on the
glacier surface are explored for use in this study, including
traditional linear precipitation lapse rates, exponential lapse
rates and multivariate models based on regional snow data
accumulation at Haig and Peyto Glaciers. We parameterize
glacier snowpack based on valley-bottom precipitation
measurements at a central location in the Bow basin, Banff,
which has an elevation of 1397m. The final model choice is
described in detail below.
Summer snowfall also plays an important role in the
model, particularly for estimating albedo. A study of summer
precipitation lapse rates in the Eastern Canadian Rockies
yielded no statistically significant results (Shea and others,
2004), which suggests that orographic controls on summer
precipitation are weak in this region. Summer snowfall data
available for this study are limited to Haig Glacier, which is
likely not representative of snowfall over the entire basin. As
an alternative, summer precipitation over the basin is
modelled as equal to precipitation recorded at Banff.
Snowfall is assumed to occur when elevation-lapsed
temperatures are <08C. The performance of this assumption
is examined at the Haig Glacier AWS for 2002–03 using a
confusion matrix and by calculating the percentage differ-
ence in total snowfall for both summers.
Radiation absorbed at the glacier surface is estimated
based on three separate models. First, daily potential radi-
ation is calculated for each point on the glacier surface, then
modified by a cloud cover factor to estimate incoming solar
radiation. The absorbed radiation is then estimated through
a modelled surface albedo. This modelled absorbed radi-
ation at each point on the glacier is input into the melt
model described in Eqn (1).
A well-established method for calculating potential direct
solar radiation, IP, is laid out in Oke (1987). It relies on
geographic information available through the DEM, the date
and the time of the calculation. The equations are
IP¼I0
Rm
R
2
a
P
P0cos Z
cos ð3Þ
cos ¼cos b
cos Zþsin b
cos Zðsun slopeÞ ð4Þ
In Eqn (3), I0is the solar constant (1368 W m
–2
), ðRm
RÞ2is the
eccentricity correction factor of the Earth’s orbit, with Rthe
instantaneous Earth–Sun distance and Rmthe mean Earth–
Sun distance, a¼0:75 is the constant clear-sky transmis-
sivity, optimized for Haig Glacier by Schaffer (2010), Pis
atmospheric pressure and P0is mean atmospheric pressure
at sea level. The local zenith angle, Z, is calculated as a
function of latitude, hour angle and solar declination. The
hour angle is a function of the time of day (i.e. 1–24), and
the solar declination is a function of the time of year.
In Eqn (4), the effects of radiation incident on an angled
surface are accounted for, with b
being the surface slope
angle, sun the solar azimuth angle and slope the slope
azimuth angle. Solar azimuth angle is a function of
longitude, hour angle and solar declination.
For regional modelling, cloud cover over the study area is
taken directly from NCEP Reanalysis data. NCEP Reanalysis
provides cloud cover as a fraction over the entire atmos-
pheric column, fc, and potential incoming radiation is
multiplied by (1 fc) to reduce radiation incident on the
ground. Daily incoming radiation is then summed into 5 day
Bash and Marshall: Glacial melt contributions to the Bow River 141
periods for use in the model. Incoming radiation calculated
using NCEP cloud cover is compared with radiation calcu-
lated using cloud cover estimated from local data at Haig
Glacier, using a ratio of measured incoming radiation to
potential radiation in the glacier forefield. Data collection at
this site is unaffected by station movement, and the
radiometer maintains a truer horizontal position.
Glacier surface albedo is affected by a number of factors,
including snow depth, grain size, presence of impurities,
and water content (Hock, 2005). Brock and others (2000)
undertook an extensive study of albedo modelling. Based
on an analysis of different model parameters, the study
outlines a model of glacier surface albedo which relies on
snow depth and timing of snow events. For deep snow
(>11 cm w.e.) the surface albedo is unaffected by underlying
ice. Instead, albedo is controlled by snow age, which is a
proxy for grain size and concentration of impurities. Brock
and others (2000) found that for deep snow, albedo
decreases logarithmically with increasing accumulated
PDD since snowfall. This relationship changes to an
exponential decay when shallow snow depths are reached
(<11 cm w.e.). In both cases the albedo is ‘reset’ to a new
snow albedo when snowfall events occur, by resetting the
cumulative PDD. We follow this approach, with coeffi-
cients in the albedo model based on the work of Schaffer
(2010) on Haig Glacier. The albedo is calculated as a 5 day
average based on 5day melt from the previous period, daily
snow accumulation and daily accumulated positive tem-
perature. Daily snow accumulation is used to reset
accumulated PDD, in order to capture mid-period changes
in albedo. We specify a fixed albedo of 0.23, based on late-
summer (bare ice) albedo at the Haig Glacier AWS during
the summers of 2002–04.
Temperature for degree-day melt models is most com-
monly estimated using a reference station (Banff, in our case)
along with linear lapse rates to adjust for cooling with
elevation. A number of studies report average environmental
lapse rates in mountainous regions (e.g. Martinec and
Rango, 1986; Rolland, 2003; Lundquist and Cayan, 2007).
For this study, monthly summer lapse rates are calculated
using average temperature from seven weather stations,
including two AWS sites at Haig Glacier and five Environ-
ment Canada monitoring stations. Lapse rates are deter-
mined for May, June, July and August, from 2002 to 2004.
The final lapse rates are taken as an average of each month
over the three years.
Glaciers have cooling effects on temperatures. Glacier ice
and snow temperatures are held at 08C while melting
occurs, which in turn lowers near-surface air temperatures.
Flowers and others (2005) use this knowledge to determine a
constant T, to represent the near-surface air temperature
cooling effect. A similar approach is undertaken in this
study. A correction factor is calculated, in conjunction with
the lapse rates described above, by optimizing the Nash–
Sutcliffe statistic comparing modelled and measured tem-
peratures on Haig Glacier. Daily average and maximum
temperatures, b
Tavg and b
Tmax, are modelled using the
modified lapse rate described above.
PDD are calculated most accurately using hourly or sub-
hourly timescales. Without this resolution, days with average
temperatures below 08C will have no modelled PDD,
whereas in reality some period of the day may have positive
temperatures. Reeh (1991) used a sine function to model
annual temperature distribution for the purpose of
degree-day modelling. In this method, the sine curve
describing temperature distribution is centred around the
average temperature, with an amplitude equal to the range
between the maximum and average. Schaffer (2010) models
daily temperature distribution at Haig Glacier using the same
method. Schaffer (2010) introduces a lag of 6 hours in order
to match data obtained at Haig Glacier for the daily tem-
perature cycle (Eqn (5)). This shift was also used in this study.
TðtÞ ¼ b
Tavg b
Tmax
2cos ð2ðt=tT0:25ÞÞ ð5Þ
where trefers to the hour of the day and tT¼24 is the total
hours in the day.
To calculate PDDres, temperatures calculated in Eqn (5)
between 08:00 and 20:00 are modified to remove the
influence of absorbed radiation. Temperatures between
08:00 and 20:00 are left as calculated. Once a new daily
distribution is determined, positive temperature hours are
summed into modelled residual PDD and used as input for
the melt model.
Modelled variables isolated at the Haig Glacier AWS
location are compared to measured variables during
summer 2007.
RESULTS
Calibration and model performance
The correlation between average daytime temperature and
absorbed solar radiation at the AWS for the summers of
2002–04 is 0.70. Linear regression is used to find the
coefficients and for computing Tres. Equation (6) is the
tuned model used to compute the influence of radiation on
temperature.
TI¼0:67Iabs 0:240 ð6Þ
After removing the influence of absorbed radiation, the
correlation between Tres and Iabs is reduced to almost zero,
showing that residual temperature is not correlated with
absorbed radiation.
Using ordinary least-squares regression and employing
the residual temperatures calculated from Eqn (6), Eqn (1) is
calibrated with 2002–04 summer data from the glacier AWS.
The calibrated model is given by
M¼3:0PDDres þ2:1Iabs 33:9 : PDD >0
0 : PDD 0
ð7Þ
where Mrefers to total 5 day melt (mm w.e.) based on
cumulative absorbed radiation and PDDres over 5 day
periods. While the constant intercept in this equation
theoretically permits ‘negative’ melt, this situation does not
arise because 5 day absorbed radiation and PDDres totals are
always well above zero at times when PDD> 08C d.
The model is tested by calculating melt using an
independent dataset from summer 2007 (Fig. 2). The model
overestimates melt for some 5 day periods, particularly in
late summer, while underestimating in other 5day periods
(e.g. in May). The average absolute error is 34.3 mm w.e. for
a 5 day period, which corresponds to an average deviation of
30%. Overall the model under-predicts melt by 10% for
summer 2007. The Nash–Sutcliffe coefficient is found to be
0.65 (Table 1). This value indicates the model accounts for a
larger portion of the variability in measured melt than the
average melt value for the season. By contrast, a negative N
Bash and Marshall: Glacial melt contributions to the Bow River142
value would indicate that average melt would be a better
predictor of melt than the model, for a given 5 day period.
With the correlation between absorbed radiation and
temperature removed, the influence of each variable on melt
can be examined. On average, 80% of summer melt is
attributable to absorbed radiation. The remaining 20%
comes from residual temperature, the proxy for other terms
in the energy-balance equation. The influence of tempera-
ture peaks in July when residual PDD is highest and
absorbed radiation has not yet reached its maximum. In
May, temperatures are often below freezing, and melt is
almost entirely due to absorbed radiation.
For comparison purposes the 2002–04 data from Haig
Glacier are also used to calibrate the model described by
Pellicciotti and others (2005). Summer 2007 data are then
used to test the model against measured melt as well as melt
modelled using Eqn (7). The results of the model run are
summarized in Table 1. The two melt models perform
equally well, with the same Nash–Sutcliffe coefficient and
similar errors.
Distributed model evaluation
The distributed model is initialized using modelled snow-
pack and applied over Haig Glacier for the 2007 melt season
using modelled inputs. Modelled variables isolated for the
location of the Haig Glacier AWS are evaluated through
comparison with measured data (Figs 3 and 4). Statistical
results are summarized in Table 1. The Nash–Sutcliffe
statistic is slightly lower (N¼0:59) than that of the point
models described above, indicating the model still performs
better than assigning an average melt value for each period.
The model overestimates melt by 4% and has an average
absolute error of 36.8 mm w.e. (5 days)
–1
(Fig. 3d).
Initial snowpack
As described above, several models were explored for
estimating 1 May snowpack at both Haig and Peyto
Glaciers. A linear lapse rate model captures average
snowfall at both glaciers, lacks the steep gradient observed
in snow depth over glacier surfaces and the inaccurate
distribution of snow poses problems for model performance.
While an exponential lapse rate is able to produce a steeper
gradient of snow accumulation, predicted snowfall at high
elevations is greatly overestimated. Instead, a multivariate
model using winter (October–April) precipitation in Banff
(PB, mm) and elevation, z(m), is fit to 1 May snow
distribution along the centre line of Peyto Glacier. The
optimized fit to winter balance data at Peyto Glacier, bwðzÞ,
has an R2¼0:82 and the final model is given by
bwðzÞ ¼ 1:17zþ2:17 PB2496 mm w.e. ð8Þ
The model is applied at Haig Glacier for the summers of
2004 and 2005. The comparison reveals lower correlation
along the centre line than Peyto Glacier, R2¼0:35 in 2004
and R2¼0:20 in 2005 (Fig. 5). Wind redistribution at Haig
Glacier creates a highly irregular distribution pattern which
is unlikely to reflect snow cover elsewhere in the basin
(Fig. 5). This approach is obviously too simple, but few data
on high-elevation snowpack are available to refine this
further, given the local nature of wind redistribution. The
model is used to compute winter balance at both glaciers for
comparison to measured winter balance. Winter mass-
balance data are available from Haig Glacier from 2002–05
and 2009–13. For these years, modelled winter mass
balance has a bias of –290 mm w.e. Winter balance at Peyto
Glacier was computed for 1985–95, and the mean bias for
this period is –50 mm w.e. Because the majority of glaciers
in the Bow River basin are in closer proximity to Peyto
Glacier than to Haig Glacier and the elevation range of
Peyto Glacier is more representative of the basin hyp-
sometry, Eqn (8) is used to simulate winter snowpack on all
the glaciers of the basin.
Incoming solar radiation
Figure 4c shows 5 day totals of measured and modelled
incoming solar radiation at Haig Glacier during 2007 for the
Table 1. Performance of three melt models at the Haig Glacier AWS using summer 2007 data
Summary statistic Tres point Pellicciotti model Distributed Tres Distributed Haig radiation Observations
Nash–Sutcliffe (N) 0.65 0.65 0.59 – –
Avg error (mmw.e.(5 days)
–1
)34.3 33.7 36.8 – –
Total error (%) –10.4 –8.5 3.7 – –
Total snow and ice melt (mm w.e.) 2228 2270 2574 2766 2482
Avg daily I(MJ m
–2
d
–1
) 22 – 18 22 22
Avg albedo 0.59 – 0.54 0.56 0.59
Avg Iabs 45 – 40 47 45
Avg T(8C) 5.2 – 4.4 4.4 5.2
Avg PDD (5 day total; 8C d) 24 – 26 26 24
Avg PDDres (5 day total; 8C d) 9.0 – 16.6 14.6 9.0
Fig. 2. Predicted and measured 5 day melt totals at Haig Glacier
during the 2007 melt season.
Bash and Marshall: Glacial melt contributions to the Bow River 143
distributed model. The correlation between measured and
modelled daily incoming radiation is 0.23. The general
patterns of daily and seasonal variability are still present, but
the modelled daily average incoming radiation is 18% less
than observed (22 and 18 MJ m
–2
d
–1
, respectively). NCEP
cloud cover leads to too much attenuation of incoming
radiation in summer 2007. A separate simulation, using
cloud cover estimations from Haig Glacier in place of NCEP
cloud cover, has a correlation between measured and
modelled radiation of 0.91, a large improvement that is
expected using locally derived cloud cover estimates. The
average daily value is 22 MJ m
–2
d
–1
, in accordance with
observations, and total melt at the AWS is 2766mm w.e.,
200 mm greater than the simulation using NCEP cloud cover.
Albedo
The modelled albedo shows the overall trend of measured
albedo (Fig. 4d). The model is also able to capture the
response to summer snowfall events, seen through the
correspondence of spikes in albedo to new snow. Early- and
midsummer albedo are generally underestimated, while
late-summer ice albedo is higher than measured. The overall
average albedo is lower than measured, 0.54 and 0.59
respectively.
Summer snow events
Summer snow events, which feed into the albedo model, are
assessed using a confusion matrix comparing the timing of
modelled snow events to that of measured events during the
summers of 2002 and 2003, independent of magnitude. The
model predicts timed snow events correctly 61% of the time.
Coincidentally, the number of total modelled snow events is
equal to the number of measured snow events. The total
modelled summer snowfall for the two summers is
124 mm w.e., which represents only 25% of the total
measured summer snowfall for these summers. Total snowfall
in the 2007 model run is closer to measured, 105 mm w.e.
compared to 122 mm w.e.
Absorbed radiation
Modelled albedo and incoming radiation both feed into the
calculation of absorbed incoming radiation, which is an
essential input to the melt model and the calculation of Tres.
The model tends to underestimate absorbed radiation
throughout the summer (Fig. 3c); overall Iabs is under-
estimated by 8.7%. This is a result of the underestimation of
incoming radiation (Fig. 4c), but the impact is partially
compensated by the lower average albedo in the model.
The average 5day absorbed radiation from the model is
Fig. 3. Measured vs modelled input fields for the radiation–temperature melt model for 5 day periods from 1 May to 30 September 2007.
(a) Positive degree-days (PDD); (b) residual PDD; (c) incoming (asterisks) and absorbed (diamonds) solar radiation totals; and (d) snow/ice
melt. Each plot shows 1 : 1 lines.
Bash and Marshall: Glacial melt contributions to the Bow River144
40 MJ m
–2
, compared with 45 MJ m
–2
for measured absorbed
radiation.
Near-surface air temperature
Monthly air temperature lapse rates developed for this study
range from –0.0060 to –0.00558C m
–1
. Using these lapse
rates, the temperature shift, T, is calculated for the period
2002–04. The efficiency statistic is optimized, with a value
of 0.69, and the temperature correction T¼ 0:688C.
Daily average temperatures simulated using the lapse rate
model and Tare lower on average than the measured
temperature at Haig Glacier for summer 2007, 4.48C and
5.28C, respectively.
The lapse rate model was used to calculate daily average
and maximum temperatures on the glacier for use in Eqn (5).
Modelled PDD showed no significant bias to over- or
underestimation (Figs 3a and 4a). The average modelled
PDD for 5 day periods in summer 2007 was 268C d, while
the average of measured PDD was 248C d.
Residual air temperature
Residual temperature, calculated from modelled air tempera-
ture and absorbed radiation as outlined above, is aggregated
into residual PDD. The residual PDD are overestimated by
the model (Figs 3b and 4b). The average modelled and
measured values for PDDres for 5 day periods in the 2007
Fig. 5. Measured and modelled winter snowpack using a linear function at Peyto and Haig Glaciers.
Fig. 4. Measured (black) and modelled (green) input fields for the radiation–temperature melt model, 1 May to 30 September 2007. (a) 5 day
PDD totals; (b) residual 5 day PDD totals; (c) 5 day incoming solar radiation totals; and (d) albedo. The orange line in (d) shows the daily
albedo data, and the black line is the 5 day average. Diamonds indicate the modelled fresh-snow events (right axis).
Bash and Marshall: Glacial melt contributions to the Bow River 145
season are 16.6 and 9.08C d. The highest error occurs in July,
coinciding with the highest temperature errors and an
extended period of underestimated incoming radiation.
Melt simulations
Modelled discharge is compared to discharge based on
mass-balance surveys from 2004 and 2005 at Haig Glacier.
The model underestimates total discharge by 17% and 21%
in 2004 and 2005, respectively. A comparison experiment
was made initializing the model with measured winter
snowpack in both years. In these experiments, total runoff is
underestimated by similar amounts, 18% and 21%.
Modelled winter mass balance at the terminus of Haig
Glacier is higher than measured for 2004, while at higher
elevations snowpack is underestimated (Fig. 6a and b).
Initializing the model with estimated snowpack produces
less melt at the terminus than model runs initialized with
measured snowpack; while at higher elevations modelled
snow produces more melt than measured (Fig. 6c and d).
The difference in accumulation between the measured and
modelled simulations shows a similar spatial pattern to the
difference in net balance between the two simulations,
where underestimated accumulation corresponds to over-
estimates of melt and vice versa.
Given the close agreement between total runoff using two
snowpack initializations in both 2004 and 2005, the over-
and underestimations caused by the simplistic snowpack
model used here balance out at Haig Glacier, at least for
these two years. This relationship suggests that overall the
model underestimates runoff, even when the error associ-
ated with initial snowpack is removed. This underestimation
is in contrast to results reported above for 2007 where
glacier melt is overestimated (Table 1).
The model is also run for the 1993–95 summer melt
seasons for comparison to net balance at Peyto Glacier. In
1993 and 1994 the model underestimates net balance by
27% and 15%, respectively, whereas in 1995 it overestimates
net balance by 5%. The large underestimation in 1993 is
likely due to improper specification of initial snowpack,
while modelled snowpack in 1994 and 1995 is closer to
measured depths. The year-to-year pattern in modelled melt
is consistent with what can be expected given the initial
snowpack (i.e. more melt with less initial snow and vice
versa). The correlation between melt and initial snowpack
indicates the important role of albedo in affecting summer
runoff, which is generally captured in the model.
BASIN-WIDE GLACIAL MELT
The distributed melt model is used to compute total glacial
melt throughout the headwaters of the Bow River for the
years 2000–09. The following analysis considers monthly
discharge in Calgary and monthly ice melt.
Table 2 summarizes summer (June–September) melt and
discharge statistics for the years 2000–09. A monthly
breakdown of glacial runoff reveals that the highest contri-
bution from glacial ice melt comes in August (Table 3). The
August contribution is two to nine times higher than that of
July. We assume here that 100% of runoff is routed through
the Bow River in the same month in which it melts. In reality,
a portion of glacial runoff may be delayed through ground-
water infiltration, and an additional amount may be lost due
to evaporation.
The four years with the lowest summer discharge in
Calgary, 2001, 2003, 2006 and 2009, stand out as
coinciding with three of the highest years of ice melt (Table
Fig. 6. (a, b) Winter mass balance (May snowpack; common colour bar) and (c, d) net mass balance (common colour bar) on Haig Glacier,
2003–04. (a, c) Measured data; (b, d) from the regional distributed model.
Bash and Marshall: Glacial melt contributions to the Bow River146
2; Fig. 7). These years also have the highest ratio of ice melt
to total melt (Table 3). In these years ice melt represents
5.1–6.0% of summer discharge in Calgary. September ice
melt in 2009 is considerably higher than in other years and
shows a higher contribution to streamflow than July and
August of the same year (Fig. 7).
In 2006, ice melt represents a significant portion of the
total annual flow in Calgary, 4.2%, as well as one of the
highest August contributions to Calgary discharge. Peak
discharge in Calgary was 3–4 weeks earlier than on average,
during the last week of May and first week of June (Fig. 8).
During 2006, August flow in Calgary was 82% of the average
August flow for the decade. Lower flows lead to an especially
high glacial contribution in July, August and September of
that year. In contrast, 2005 ice melt contributes only 1.6% of
annual discharge at Calgary. In that year, total ice melt is less
than half of the 2006 total, while total summer discharge in
Calgary was 5% greater than in 2006.
For comparison with discharge reported in Hopkinson
and Young (1998), a brief summary of modelled summer
(June–September) discharge from glaciers above Banff is
given in Table 4. In this table and Table 2, glacier volume
change (i.e. net mass balance) is included for better
comparison with previous studies. In years of negative net
balance, net mass balance and ice melt are similar (<10%
difference), except in the case of 2005. Unusually high
summer snowfall in 2005 contributes to a less negative net
balance in that year.
DISCUSSION
Model performance
The model developed in this study is able to remove the high
collinearity between absorbed radiation and air tempera-
ture. When the residual temperature is used in Eqn (7), the
resultant model explains 71% of variability in melt at the
AWS on Haig Glacier, based on 5 day melt periods. Model
performance is equivalent to that of a radiation–temperature
melt model based on Pellicciotti and others (2005). Both
models under-predict the total melt at the weather station by
10% when tested against observed data from 2007, with
average errors of 30% for 5 day melt totals (Table 1).
This method is of most use in areas where degree-day
factors are highly variable over small scales, such as valley
glaciers in complex mountain environments. Pellicciotti and
others (2005) address these issues, but their modelling
approach fails to account for collinearity of the two
Table 3. Summary of glacier discharge breakdowns, 2000–09. Values above average are in boldface
Ice melt as % of Calgary discharge Total melt Ice melt Snowmelt Ice melt as % of total melt
Year May June July August September
10
6
m
3
10
6
m
3
10
6
m
3
2000 0 0.1 1.0 10.0 5.7 123 61 62 49
2001 0 0.1 2.7 15.9 15.6 147 83 64 56
2002 0 0 3.0 10.9 7.8 131 62 69 47
2003 0 0.1 5.7 19.5 15.6 166 103 63 62
2004 0 0.1 2.3 11.6 2.9 121 56 65 46
2005 0 0.1 1.7 8.6 4.7 112 44 68 39
2006 0 0.4 10.4 18.1 10.4 172 110 62 64
2007 0 0.1 3.3 12.4 7.9 152 75 77 50
2008 0 0.1 2.5 13.1 6.9 130 68 62 52
2009 0 0.2 4.1 12.7 19.4 160 101 59 63
Average 0 0.1 3.7 13.3 9.3 141 76 65 53
Table 2. Estimated annual and summer (June–September) proportions of ice melt and basin yield for the Bow River at Calgary. The lowest
basin yields and highest glacial melt are in boldface
Year Annual discharge
at Calgary
Total summer
discharge at Calgary
Total summer
ice melt
Glacier
volume loss
Yearly discharge
represented by ice melt
Summer discharge
represented by ice melt
10
6
m
3
10
6
m
3
10
6
m
3
10
6
m
3
% %
2000 2754 1909 61 57 2.2 2.9
2001 2191 1371 83 82 3.8 5.1
2002 2596 1888 62 58 2.4 3.1
2003 2641 1646 103 101 4.0 5.5
2004 2713 1770 56 53 2.1 2.9
2005 2793 1681 44 33 1.6 2.2
2006 2584 1481 110 103 4.2 5.8
2007 3032 2073 75 72 2.5 3.2
2008 2595 1691 68 64 2.6 3.5
2009 2276 1524 101 100 4.4 6.0
Average 2617 1703 76 73 3.0 4.0
Bash and Marshall: Glacial melt contributions to the Bow River 147
independent variables, temperature and absorbed radiation.
The presence of collinearity can inflate variance in regres-
sion coefficients, which introduces higher uncertainty into
model predictions (Stewart, 1987). In fact, in the presence of
collinearity, least-squares regression is no longer the best
linear unbiased estimator. This stems from the shared
information provided by both variables, which cannot easily
be separated to provide two distinct relationships with the
predictand (Belsley and others, 2004).
In light of this, the model provided in this study is an
advance because it is able to separate the influence of each
variable. In cases where a complete energy balance is not
feasible, the model presented here may be a good choice.
The required inputs are readily available and the distributed
model is physically based and easily interpreted, making it
portable to other areas.
Modelled runoff
Results of modelling from the past decade are comparable to
previous work examining glacial runoff in the Bow River
basin, which is summarized in Table 5. The three basin-scale
studies have estimates of glacier area ranging from 60 to
89 km
2
. We calculate 57 km
2
of ice based on satellite
imagery from the period 2004–06 (Bolch and others, 2010),
including all ice bodies greater than 0.1 km
2
.
For comparison between studies, annual glacial volume
loss is standardized by the total glacial coverage (km
2
).
Annual melt contributions to the basin reported in the
literature for the late 20th century range from 0.88 to
1.4 m a
–1
. The contribution calculated in this study, 1.3 m a
–1
on average, is closest to the melt calculated by Marshall and
others (2011). The lower average contribution reported by
Demuth and others (2008) and Comeau and others (2009)
may be attributed to different periods of study; glacier mass
balance in the region was more negative in the 2000s than
in earlier periods.
Relative contributions in summer are lower in this study
than reported by Marshall and others (2011), but it should be
noted that direct comparison of estimates provided in these
studies is complicated by varying definitions of the summer
melt season. In this study, melt from June to September is
included in estimates and compared to streamflow from the
same period, while other studies report summer percentages
as July–September. When June ice melt is excluded, the
average summer contribution from ice melt is 75106m3,
equivalent to 7.4% of July–September discharge in Calgary.
Average contributions to the Bow River above Banff are
significantly higher than estimates provided by Hopkinson
and Young (1998), Demuth and others (2008) and Comeau
and others (2009) (Table 6). Hopkinson and Young (1998)
Fig. 7. Summer ice melt for selected years of high and low melt,
2004–06 and 2009. Fig. 8. Ice melt and Bow River discharge at Calgary for 2006. This is
the year of highest melt between 2000 and 2009.
Table 4. Estimated annual proportions of ice melt and basin yield for the Bow River in Banff
Year Yearly discharge
represented by ice melt
Total summer discharge
at Banff
Total summer ice melt Glacier volume loss Summer discharge
represented by ice melt
% 10
6
m
3
10
6
m
3
10
6
m
3
%
2000 3.7 867 44 40 5.0
2001 6.7 608 61 41 10.0
2002 4.2 856 46 43 5.3
2003 6.9 740 77 75 10.3
2004 3.6 800 42 39 5.2
2005 2.7 757 33 24 4.3
2006 7.4 661 81 76 12.2
2007 4.2 945 55 53 5.8
2008 4.5 762 49 46 6.4
2009 8.0 682 75 51 11.0
Average 5.2 768 56 49 7.6
Bash and Marshall: Glacial melt contributions to the Bow River148
provide a breakdown showing annual glacier contributions
to the river ranging from –3.7% to 13.2%, where negative
percentages indicate years of positive net balance. In the
early period of the study, the authors show more glacier
storage than depletion, but from 1980 to 1993 the average
contribution is 3.6%. For the same period they report
average annual glacier volume losses of 42:3106m3a
–1
.
This is more comparable to the average ice melt we have
calculated in this study, 48:7106m3. Demuth and others
(2008) and Comeau and others (2009) do not provide an
annual breakdown, so it is difficult to compare directly with
our estimates.
In the past decade the highest ice melt coincided with
years with low discharge in Calgary. In these years the
proportion of annual and summer discharge attributed to ice
melt is high. Hopkinson and Young (1998) found similar
results between 1952 and 1993. The concurrency of low
total discharge and high glacial melt ties in with the
relationship between snowfall and mass balance discussed
above, and is related to the persistence of warm, dry high-
pressure ridging events in these summers. Such weather
systems give both reduced summer precipitation and
increased glacier melt. In a snowmelt-dominated river such
as the Bow, low winter snowpack means low river flows.
These years commonly correspond to years of especially
high ice melt on the glacier, leading to the increased
percentage contribution to streamflow.
September 2009 serves as a good example of the
limitations of running the model only from May through
September. In that year, September discharge is exception-
ally high and melt does not shut off by the end of the month.
Field visits in late September that year revealed exposed ice
over the entire glacier surface at Haig Glacier. While this
pattern is atypical during the study period, it will likely
become more common in the future and this pattern should
be taken into consideration when modelling glacier runoff.
This problem is easily solved by running the model for the
full year, allowing accumulation and melt to be determined
by temperatures, rather than arbitrary calendar dates.
Representativeness of field calibration sites
We assume that climatological conditions and mass-balance
processes at Haig and Peyto Glaciers are representative of the
Bow basin. This is difficult to confirm without additional field
data, as no meteorological or glaciological data are available
from other glaciers in the basin. From available data, though,
there is no reason to believe that either Haig or Peyto Glacier
is climatically unusual. They are near the southern and
northern edges of the basin, bracketing most of the other ice
masses. Each glacier has an accumulation area on the
continental divide, along with median elevations and aspects
that are representative of glaciers in the Bow basin. Snow
accumulation totals are similar at each site, with average
specific winter balances of Bw¼1195 290 mm w.e. at
Peyto Glacier (1966–95; Demuth and Keller, 2006) and
Bw¼1320 295 mm w.e. at Haig Glacier (2002–13; un-
published data). Data periods do not overlap, unfortunately,
but this constitutes all available winter mass-balance data at
the two sites. Peyto Glacier is not anomolously snowy for the
region, despite its size. Rather, glaciers within the basin are
concentrated in the continental divide region, where they
exist due to the high snow accumulations delivered by moist
Pacific air masses that intersect the Rocky Mountains.
We assume that summer melt-season processes work the
same way throughout the basin, based on the Haig Glacier
model calibration. Because the melt model is physically
based, and solar radiation can be modelled as a function of
local terrain, we argue this is a reasonable assumption, but
we are not able to test it with available data. One of the main
uncertainties is whether albedo values at Haig Glacier are
representative of other glaciers in the basin. Published snow
and ice albedo values for Peyto Glacier are similar to those at
Haig Glacier (Cutler and Munro, 1996), supporting our
assumption that the Haig Glacier melt model is portable
Table 5. Summary of Bow basin glacier studies
Demuth and others (2008) Comeau and others (2009) Marshall and others (2011) This study
Region S. Saskatchewan Bow River (Calgary) Bow River Bow River (Calgary)
Time period 1976–98 1975–98 2000–07 2000-09
Glacier area (km
2
) 88.4 10 89 (1998) 60 57
Glacier volume (km
3
) – – 3.0 2.0
Standardized annual volume loss (m a
–1
) 0.96 0.88 1.4 1.3
Flow contribution
Annual (%) – 2.8 2.8 2.8
Summer (%) – – 6.7 (Jul–Sep) 3.8 (Jun–Sep)
Table 6. Summary of studies of glaciers above Banff
Hopkinson and Young (1998) Demuth and others (2008) Comeau and others (2009) This study
Time period 1952–93 1976–98 1975–98 2000–09
Glacier area (km
2
) 54 – – 44
Annual melt (10
6
m
3
) 23.4 – 25.8 48.7
Flow contribution
Annual (%) 1.98 2.8 2.2 4.9
Summer (%) – 6.2 (Jul–Sep) 4.8 (Jul–Sep) 7.2 (Jun–Sep)
Bash and Marshall: Glacial melt contributions to the Bow River 149
within the basin. A second question is whether the summer
temperature regime and temperature lapse rates in the
atmospheric boundary layer at Haig Glacier are represen-
tative. Katabatic winds on larger glaciers, such as Peyto,
cause cooling at lower elevations in these environments, and
other local terrain effects (e.g. shading) affect summer
temperature. Katabatic winds are weak and intermittent at
Haig Glacier and are drowned out by topographic funnelling
of synoptic-scale winds, which are frequently strong.
Because most glaciers in the Bow basin are smaller than
Haig Glacier and in similar meteorological and topographic
environments, this may make it a suitable reference site.
Additional field data are needed to examine this.
Model uncertainties
The melt model is nonlinear, and multiple sources of error
propagate through the model, including uncertainties in the
initial snow depth, near-surface air temperature, albedo, and
incoming solar radiation (with errors primarily due to poor
estimation of cloud cover/effective atmospheric transmissiv-
ity). These errors are mutually dependent; for instance, error
in the initial snow depth leads to improper albedo evolution
(transition from snow to ice), which affects absorbed
radiation and, in turn, the residual temperature calculation.
It is therefore difficult to isolate the error arising from each
component of the model, but we can assess the overall model
performance for Haig and Peyto Glaciers through compari-
son with summer mass-balance data. This provides an esti-
mate of the ‘bottom line’ in terms of model errors and biases.
Based on this approach, a negative bias is evident in the
melt model (tendency to underestimate summer melt), and
modelled summer mass balance for individual years has an
error of up to 27%. For the years that we test, two melt
seasons on Haig Glacier and three on Peyto Glacier, total
summer melt is underestimated for four summers (average of
20%) and overestimated for one (+5%), giving a mean bias
of –15%. Haig Glacier simulations with in situ vs far-field
(‘degraded’) model inputs indicate that modelled tempera-
ture and incoming solar radiation are both significant
sources of error. For our calibation period (summer 2007),
modelled incoming solar radiation is only 82% of observed,
and mean modelled temperature is 0.88C too low. Both of
these influences contribute to the model bias.
Snow depth and estimated cloud cover stand out as the
two greatest sources of uncertainty in modelled variables, as
they both affect the amount of absorbed radiation at the
surface. Model runs at Peyto and Haig Glaciers highlight the
sensitivity of the model to initial snowpack conditions. Two
effects can be seen from differences in initial snowpack: an
influence on glacier mass balance and the influence
on albedo.
Higher winter snowpack leads to more positive mass
balance and hence less ice melt contributing to river flows.
With a higher snowpack, ice is exposed later in the summer
than when winter snowpack is lower. In these years, shorter
ice exposure before the onset of new snow cover decreases
the total amount of melt contributing to the river. Con-
versely, when winter snowpack is low, low-albedo ice is
exposed longer. With winter balance already being lower in
these years, increases in melt push net balance even lower.
Simulations at Haig and Peyto Glaciers show the greatest
discrepancy between measured and modelled melt in years
when snowpack is greatly overestimated, particularly at the
terminus (i.e. 2005 and 1993, respectively). In 2007,
modelled snowpack at Haig Glacier AWS is only marginally
higher than measured, 90 mm w.e. In these model runs,
albedo estimates closely track with measured albedo and
melt is overestimated by 4%.
The performance of the model at the distributed scale is
limited by a simplistic snowpack model. The model under-
estimates winter mass balance at both Haig and Peyto
Glaciers, with a mean bias of –291 and –50 mm w.e.
respectively. As discussed above, this underestimation tends
to inflate modelled melt through longer ice exposure. The
model is also unable to capture snow distribution patterns
seen at Haig Glacier (Fig. 5). In order to improve model
accuracy, a distributed snowpack model for the region
should be incorporated. Variability in snow distribution is
highly dependent on local winds, orographic lifting and air
moisture content (Liston, 2004). While the model used here
attempts to capture the general increase in snowpack with
elevation, snow redistribution due to wind is not accounted
for. Moreover, our reference station, Banff, is on the lee side
of the Rocky Mountains, where it is much drier; the high-
mountain snowpack in the region is influenced by the
westerly air masses that deliver orographic precipitation on
the windward slopes and on the continental divide. We
recommend that in future work the upslope precipitation
process should be physically modelled, along with wind
transport and redistribution, to improve on the glacier
snowpack model. Regional-scale meteorological models or
linearized orographic precipitation models (e.g. Smith and
Evans, 2007; Jarosch and others, 2012) are both potentially
viable ways to model snowpack in more detail. The
importance of wind redistribution can be seen in snow
accumulation patterns at Haig Glacier, which are similar
and nonlinear year after year. Regional blowing-snow
models are not available yet, but catchment-scale models
have been tested (e.g. Winstral and others, 2002; Mac-
Donald and others, 2009). Winstral and others (2002) found
snow accumulation at a catchment scale is better predicted
by the addition of upwind topographic characteristics, such
as degree of exposure and slope breaks, to more commonly
used parameters of slope, elevation and radiation input.
These models have yet to be tested at larger scales.
Modelling incoming solar radiation based on a cloud
factor is also problematic for model performance; intro-
duction of NCEP cloud cover reduces incoming radiation by
18% at the Haig Glacier AWS compared to radiation
modelled using local cloud cover estimates. Cloud forma-
tion is a complex interaction of many meteorological
variables, which are difficult to model regionally or to
assess from satellite imagery at the temporal and spatial
scales of alpine glacier energy-balance modelling. In add-
ition to cloud coverage, the type and height of cloud has
varying effects on shortwave radiation reaching the ground
(i.e. high clouds absorb less radiation than lower clouds).
This distinction is not captured in the NCEP data, which are
a total cloud cover fraction. A high-resolution meteoro-
logical model or a high-density monitoring network are
likely the only ways to accurately capture cloud cover. These
are both impractical solutions for regional modelling,
however. The only current options are statistical treatments
of cloud cover, which are effectively similar to what we
implement here, or parameterizations based on measured
variables such as daily temperature range (Dai and others,
1999). Average summer cloud conditions appear to be
reasonably captured with NCEP cloud cover, but detailed
Bash and Marshall: Glacial melt contributions to the Bow River150
hourly and daily conditions are poorly simulated. Satellite
imagery could be helpful for historical mass-balance and
melt modelling, but we are interested in developing
methods that can be applied to future forecasts, using, for
example, large-scale cloud conditions from climate models.
One fortuitous feature of the model is that there is a built-
in ‘buffer’ (negative feedback) in the propagation of errors
associated with absorbed solar radiation. Underestimates of
absorbed solar radiation give residual temperature values
that are too high, since Tres TIabs. Hence, PDDres
estimates are too high when Iabs is too low; this is a
compensating error, such that the estimated melt,
MF PDDres þRF Iabs, has less error than that of Iabs , and
possibly a different sign. In the case above, for instance,
PDDres is 84% too high (Table 1), despite lower tempera-
tures, and modelled melt at the AWS site is 4% more than
observed. This systematic compensation means that errors in
cloud cover and albedo are buffered rather than amplified,
although it leads to the concern that reasonable model
performance can mask serious errors in input data or model
parameters.
Overall, our model experiments indicate that the
combined error in the snowpack and melt modelling is
about –15%, with the negative bias indicating that we
underestimate total summer melt. Errors for individual melt
seasons range from –27% to 5%. There is negligible bias in
modelled summer melt at the Haig Glacier AWS site, where
the model was calibrated, but errors in 5 day melt totals at
the AWS site are 30%.
CONCLUSIONS AND FUTURE WORK
The model developed in this study improves on the work of
Pellicciotti and others (2005) by addressing the collinearity
between air temperature and absorbed radiation in the
glacier boundary layer. Without this improvement, linear
combinations of temperature and radiation may result in
unstable models and high sensitivity to data subset selection.
There is room for improvement in modelling the statistical
relationship between temperature and absorbed radiation,
but the uncertainties in this regression are probably minor
compared with the larger uncertainties associated with
modelling of the initial snowpack, albedo, and cloud cover.
Tested against field data from summer 2007 at the Haig
Glacier AWS site, the model simulates 5day melt totals
reasonably well (N= 0.65), with a total error of 10% over the
melt season. Applied to the entire glacier in two other melt
seasons, 2004 and 2005, the distributed melt model under-
predicts melt by 20%. We find similar estimates of model
accuracy when predicted melt is compared with available
summer mass-balance data from Peyto Glacier. Accuracy is
degraded through the introduction of the regional-scale
climate forcing, which uses NCEP cloud cover, particularly
for short-term (i.e. daily) melt modelling, but the regional
model works well for predictions of total melt-season runoff
in the historical period.
The model is limited by a simplistic method of modelling
snow accumulation. Total melt is highly sensitive to initial
snowpack as well as summer snowfall timing. A realistic
estimate of winter snow accumulation and a realistic
derivation of summer snowfall from global climate model
predictions are critical for accurate future melt estimates.
Despite potential drawbacks, the model performs reason-
ably well in reconstructing past melt at Haig Glacier.
Application of the model to two widely separated glaciers,
Peyto and Haig, demonstrates the portability of the model
and its utility in regional-scale modelling. In light of runoff
estimates that are similar to those of other studies of glaciers
in the Bow River, we believe the model is able to accurately
estimate basin-scale runoff.
Average modelled ice melt from glaciers in the Bow River
basin from the past decade is 76 106m3a
–1
. Ice melt
accounts for 4.0% of summer discharge in Calgary on
average, but reaches 5.8% in 2006. The same year, glacial
ice melt was equivalent to 18% of discharge in the Bow
River at Calgary during August, and flows in Calgary were
18% lower than average. On average for the period 2000–
09, we estimate that glacier runoff due to melting ice and
firn contributes 13% to the Bow River runoff in Calgary in
August. September contributions are also high, 9% on
average. This is the runoff associated with melting of glacier
ice; on average, this represents 50% of the total runoff
from glaciers, but most of the runoff in the early melt season
(May–July) is associated with the seasonal snowpack. These
values support previous studies, which have found glacial
melt contributions to be most important in late summer and
years of low total flow. The findings of this and other studies
of the Bow River basin show the importance of glaciers as
reservoirs in mountain environments.
Future work will focus on projecting glacial melt volume
into the coming century by coupling the melt model with a
dynamic model of glacier evolution.
ACKNOWLEDGEMENTS
We thank the Natural Sciences and Engineering Research
Council (NSERC) of Canada for support of the field studies at
Haig Glacier. The University of Calgary and the Western
Canadian Cryospheric Network, funded by the Canadian
Foundation for Climate and Atmospheric Sciences, provided
graduate support to E. Bash. We are grateful to S. Adhikari
for his input to the manuscript. We thank the two anony-
mous reviewers and the associate editor, D. MacAyeal, for
helpful insights and suggestions.
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